Lifting Surface Method Research Articles

The aerodynamics of the compound helicopter configuration

AbstractA computational method has been developed to investigate the aerodynamic interaction between a helicopter rotor and the fuselage in steady-state level forward flight. In order to model a compound helicopter the fuselage is fitted with wings. The model uses deformable vortex rings for the rotor wake, a source panel representation of the fuselage and a lifting surface method for the wings which can handle arbitrary geometries. The wake representation is based on a free wake analysis, relaxing the nodal points on the vortex rings and wing wake elements according to the induced velocities in the flow field after every time step. In this way, neither wake is restricted to planar shape. At each time step the fuselage and wing forces were calculated. The trim attitude of the fuselage was determined by the pressure field surrounding it using a potential flow model for the external flow and a fully developed turbulent boundary layer model on the fuselage surface. Parametric studies were carried out to determine the influence of wing position, wing span, wing angle of incidence and advance ratio on the results. The computer program incorporates a graphical postprocessing output routine allowing the visualisation of the wake shape, the induced velocity and the angles of incidence on the rotor disc to be made, together with the velocities at various wing stations and the lift coefficients along the span.

Unsteady subsonic aerodynamics for bodies and wings with external stores including wake effect

An unsteady subsonic method has been developed for aerodynamic computations of any elastic or rigid aricraft with external stores. The method consists of two integral parts: a body surface panel method (SPM) and a constant-pressure lifting surface method, which is the subsonic parallel of the HGM (or the ZONA51 code) for unsteady supersonics. The body considered can be flat-based or close-ended and its geometry input is amenable to any given fuselage or store configuration. The present method is considered an advancement over the past development at least in three aspects: (1) correct unsteady boundary condition on body, (2) a new wake model to account for the body/wake effect and (3) improved accuracy in wingbody interference. Various AGARD iifting surfaces, truncated blunt and pointed bodies and a number of NLR wing-storetiptank combinations were studied for method validation. The present method has shown substantial improvement in the pressures, stability derivatives and airloads on these configurations. For all cases considered, the present results, with or without the wake model, have consistently shown closest agreement with all measured data among existing methods. Therefore, we believe that an accurate and effective method is finally at hand for subsonic aeroelastic applications.

Numerical Solutions of Interaction Problem between Hull and Propeller of a Ship Considering the Effect of Free Surface

The present paper deals with the interaction problem between the hull and the propeller of a ship advancing at a constant speed on the still water surface. The Rankine source method has been employed in order to take into consideration the effect of the free surface on the hull and the propeller. The vortex lattice lifting surface method has been applied to the propeller. The interaction problem between the hull and the propeller has been solved numerically by an iterative procedure, starting from the Hess & Smith solution for the source distribution on the hull surface of the double model approximated ship as the basic flow. The effect of the interaction of the propeller has appeared on the closest hull surface as the pressure reduction and on the upper free surface as the increase of the wave just above the propeller. The calculated thrust deduction factor has showed a fairly good agreement with measured ones for 4 m and 6 m model ships.

Applying the lifting surface method to the blade tip of a hovering helicopter

The approach of inner/outer fields is applied in order to calculate the aerodynamic loads at a blade tip (inner field) of a helicopter in hovering or axial flight. It is shown that if the inner field includes the wake in the vicinity of the tip region, then the well known lifting surface method for fixed wings can be applied in order to study the aerodynamic field at the tip. This method is more efficient than other methods that have been previously applied and thus it is suitable for repeated analyses during the design procedure. Furthermore, the method is capable of dealing with complicated tip geometries without requiring excessive computer resources. Examples of using the method are presented, where the calculated results are compared with experimental ones.

HydrodynamicAnalysisofPropellersin Steady Flow Usinga Surface Panel Method

A surface panel method for the hydrodynamic analysis of a propeller operating in steady flow is described. The surface of propeller blade and hub is approximated by a number of small hyperboloidal quadrilateral panels with constant source and doublet distributions. The surface of trailing vortex sheet is also represented by hyperboloidal quadrilateral panels with a constant doublet distribution. The strength of source and doublet is determined by solving the boundary value problem at control point on each panel surface. Special emphasis was put on the Kutta condition of equal pressure on upper and lower surfaces at the trailing edge.Pressure distributions on the blade calculated by the present method are in good agreement with the experimental data. A better agreement of pressure distributions near the hub is observed when compared with those of a conventional lifting surface method. Open-water characteristics of propeller calculated by the present method are also in good agreement with experimental data.

揚力面理論による誘導抵抗の予測能力

Methods for calculating induced drag are divided into two main categories, “Near Field Method (NFM)” and “Far Field Method (FFM).” “Conventional Vortex Lattice Method (VLM)” gives not-so-good results when NFM is used, because of its poor prediction of leading-edge suction forces. Some patch-works for it have been published, all of those results however are more or less unsatisfactory; only method holding consistency and rationality may be the Quasi-VLM by C. E. Lan. This paper reports the results of the induced drag calculated by BIS (Box-In-Strip), a new numerical lifting surface method developed by the present authors. Both leading-edge suction forces in NFM and Manglertype singular integral in FFM are evaluated satisfactorily. Analytical evaluation of the induced drag for elliptical wings, in steady incompressible flow, is devised referring to the Kida's theory. BIS yields excellent correlation with analytical solutions for both of NFM and FFM on elliptic planform wings. Besides BIS gives closer agreement between the calculated results by NFM and FFM than Quasi-VLM for the general wing planforms.

A Study on the Prediction of Propeller Slipstream and the Numerical Analysis of Lifting Surface

In recent years, a highly advanced lifting surface method with high accuracy has been required in order to design the various types of propellers which demand high efficiency and to reduce ship vibration and noise.In this paper, an improved lifting surface procedure based on the vortex lattice method is presented. For the determination of a trailing vortex wake geometory, a numerical iterative procedure is described. The numerical results on propeller slipstream give a good agreement with the measured values by laser doppler velocimeter.The present method is applied to calculate the open water characteristics of a propeller. And a quasi-steady technique based on the present method is adopted to calculate the fluctuation of propeller forces and cavitation patterns behind the ship's wake field.The advantages of the present method are shown by comparing the numerical results with the experimental data of conventional and highly skewed propeller.

Iterative Lifting Surface Method for Thick Bladed Hovering Helicopter Rotors

A prescribed-wake, inviscid, incompressible, lifting-surface method using vortex sheets to define the upper and lower blade surfaces is developed to predict the pressure distribution on helicopter blades in hover. Starting with an approximate upper and lower surface vortex sheet strength distribution obtained by using a liftingline/blade-element method, the final strength distribution is computed iteratively by applying the Biot-Savart law. The convergence rate is rapid and reasonably good results can be obtained within three iterations. The method is used to compute the blade pressure distribution in hover for a single-bladed, teetering model helicopter rotor with negligible blade coning. The constant-chord, untwisted blade has a body of revolution tip and is structurally rigid. The results show good agreement with experimental data except very near the blade tip in the trailing-edge region of the upper surface where the effects of the formation of the tip vortex predominate. At spanwise stations inboard of the maximum blade bound circulation, the iterative procedure produces only small changes in the initial two-dimensional blade-element pressure distributions.

Research on Highly Skewed Propeller

Authors planned theoretical and experimental research on Highly Skewed Propeller (HSP) in order to establish advanced HSP design method which enables remarkable decrease of vibratory propeller forces, high propulsive efficiency and no problem related to blade strength.First, simplified method to calculate wake adapted skew distribution and non-linear lifting surface method to estimate propeller open characteristics were developed. These outlines are presented in this paper.Then, propeller open test (1 st, 3 rd and 4 th quadrants), self-propulsion test and cavitation test (cavity extent and thickness) were performed by using following three propellers designed for a container ship.Convensional Propeller (CP) of MAU type (MPNO. 80-3) Convensional HSP (MPNO. 80-4) Theoretically designed HSP (MPNO. 80-5) (Wake adapted skew distribution is adopted, and blade section and rake etc. are determined from the result of non-linear lifting surface calculation in order to get high propeller open efficiency.) The test results obtained are as follows;(1) Thrusts of MPNO. 80-4 and MPNO. 80-5. at astern condition are lower than that of MPNO. 80-3.Propeller open efficiency and propulsive efficiency of MPNO. 80-5 at propeller design point are about same as those of MPNO. 80-3, even though propeller open efficiency of MPNO. 80-4 at propeller design point is about 2% lower than that of MPNO. 80-3.(2) The effect of skew on cavitation characteristics related to surface force (time variation of cavity volume) was quantitatively confirmed.This research continues.The sequent reports will inform the other model test results like measurement of pressure fluctuation on a hull and measurement of stress on propeller blade etc.

Comment on "Effect of Stabilizer Dihedral and Static Lift on T-Tail Flutter"

I is reassuring in an engineering sense to see in Ref. 1 that the archaic methods of strip theory and lifting-line theory can still be made to arrive at reasonable solutions to modern problems. However, the strip theory employed in Ref. 1 lacks many of the refinements of the modified strip theory of Yates and, more significantly, it does not possess the growth potential to treat the general problem of the T-tail with partial span elevators and rudders. Hence, the experimental correlation achieved (a posteriori?) in Ref. 1 is a necessary but insufficient condition for validation of the authors' method. It would have been more informative if the authors had utilized their experimental data to evaluate modern methods for calculating the aerodynamic interference loads on the T-tail. However, before surveying these modern methods we might add four historical references on early Ttail investigations to the authors' list. The earliest applications of lifting-surface theory to the Ttail configuration were made by Stark and Davies. General discussions of interference problems have been given by Ferrari, Ashley and Landahl, Landahl and Stark, Laschka, and Ashley and Rodden. A symposium on Unsteady Aerodynamics for Aeroelastic Analyses of Interfering Surfaces was sponsored by AGARD in 1970 and eight of the fifteen papers contained in the conference proceedings were related to the T-tail problem. A comparison of results computed by different methods for wingtail-fin combinations, taken two a time, is the subject of a recent AGARD report by this commentator. Interfering lifting-surface methods contain none of the limitations on aspect ratio, taper ratio, sweep, and compressibility effects that are implicit in strip theory and lifting-line theory.! The importance of static deformation of the stabilizer should not have come as such a surprise to the authors since the change in dihedral of a wing under load factor has been recognized for many years (although not in the stability and control textbooks) as an important aspect of lateraldirectional motion at limit load factor. This was first considered by Lovell in 1948, and an analysis of the problem by lifting-surface methods was outlined by this commentator in 1965; Ref. 20 also contains some experimental correlation but only with an earlier simplified method and not with a lifting-surface method. The fact that the dihedral effect of a flexible wing typically doubles at limit load factor suggests that the stabilizer trim load is an essential parameter in T-tail flutter analysis, as the authors of Ref. 1 eventually observed. A final criticism of Ref. 1 is the authors' inconsistency in treating the rotary effects of the stabilizer. The rolling moment due to yawing was included, but the yawing moment

The Application of a Lifting-Surface Method to Large, Steady or Oscillating Models in Subsonic, Closed, Open or Slotted Wind Tunnels

SummaryA subsonic, lifting-surface method is extended to apply to low-frequency oscillations of wind-tunnel models, taking into account both longitudinal and lateral variations of tunnel lift interference. Rectangular sectioned tunnels with closed, slotted or open roof and floor and closed sidewalls are considered. A comparison is made between the aerodynamic derivatives obtained by this method and those calculated with the assumption that the model span is small compared to the tunnel width. Three models of aspect ratio 2.67 and different sweepback are considered in rigid pitching oscillations in tunnels of width/height ratio 2.5. The greatest differences between the results from the two methods occur for the tunnel with closed roof and floor and for the unswept planform. The least differences occur for the slotted tunnel and for the planform of greatest sweepback. The results indicate that, for models of conventional size [up to span/(tunnel width) ratio of 0.4], the “small-span” assumption is satisfactory in tunnels with slotted roof and floor and closed side walls, but not in fully closed tunnels.

Simplified Tradeoff Studies of Large Hydrofoil Ships

2 Denny, S. B., Cavitation and Open-Water Performance Tests of a Series of Propellers Designed by Lifting-Surf ace Method, Kept. 2878, Sept. 1968, Dept. of the Navy, Naval Ship Research and Development Center, Washington, D.C., pp. 39-43. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York, 1959, pp. 33-42. Boswell, R. J., Static Stress Measurements on a Highly Skewed Propeller Blade, Rept. 3247, Dec. 1969, Dept. of the Navy, Naval Ship Research and Development Center, Washington, D.C., p. 6-7. tinuous ratings, which determine maximum cruise speed Vmax, are 85% of these SHP values.) The two foil loadings considered (W/S = 800 and 1200 psf) are representative of current practical design bounds. The two propulsion types considered (propeller and waterjet) represent the limits (upper and lower respectively) of attainable propulsive efficiency 17. This matrix of 2 criteria x 3 SHP's x 2 (W/ S)s x 2 propulsor types produces 24 configurations.

Evaluation of the Downwash Integral for Rectangular Planforms by the BAC Subsonic Lifting-Surface Method

SummaryThe BAC subsonic lifting-surface method is applied to the problem of evaluating the downwash at the surface of wings of rectangular planform subjected to particular loadings and the results are compared with a set of datum results. Over 95 per cent of the wing span the results of the BAC method are shown to be accurate to within 0.01 per cent, irrespective of chordwise position.

Refinement of the nonplanar aspects of the subsonic doublet-lattice lifting surface method.

The initial formulation of the Doublet-Lattice Method has proven theoretically accurate for calculating the interference effects on arbitrary classes of oscillating nonplanar configurations with one known exception: nearly coplanar wing/horizontal-tail combinations. For this class of problems the integration of the kernel across the element loses accuracy. The reason for this loss of accuracy is explained, and a refined method for performing the required integration is presented. Numerical studies using wing-tail configurations are presented to illustrate how well the refined method works. Also a T-tail calculation is repeated to show that calculations using other configurations are unaffected by the refinement.